Elastic states of doughnut-like inclusions with uniform eigenstrains treated by averaged Eshelby tensors

The averaged Eshelby tensors that relate uniform eigenstrains and average total strains in doughnut-like inclusions are obtained. These are compared with the Eshelby tensors of oblate spheroidal and rod-like inclusions. We show that the averaged Eshelby tensors of the doughnut-like inclusions on a plane are almost the same as the average of the Eshelby tensors of randomly oriented rod-like inclusions on the same plane. This is satisfied for both 'fat' and 'thin' doughnut-like inclusions.